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Uniqueness in cauchy problems for diffusive real-valued strict local martingales

Çetin, Umut ORCID: 0000-0001-8905-853X and Larsen, Kasper (2023) Uniqueness in cauchy problems for diffusive real-valued strict local martingales. Transactions of the American Mathematical Society Series B, 10 (13). pp. 381-406. ISSN 2330-0000

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Identification Number: 10.1090/btran/141

Abstract

For a real-valued one dimensional diffusive strict local martingale, we provide a set of smooth functions in which the Cauchy problem has a unique classical solution under a local 1 2 \frac 12 -Hölder condition. Under the weaker Engelbert-Schmidt conditions, we provide a set in which the Cauchy problem has a unique weak solution. We exemplify our results using quadratic normal volatility models and the two dimensional Bessel process.

Item Type: Article
Additional Information: © 2023 The Author(s).
Divisions: Statistics
Subjects: Q Science > QA Mathematics
H Social Sciences > HA Statistics
Date Deposited: 27 Apr 2023 14:21
Last Modified: 09 Jun 2024 07:45
URI: http://eprints.lse.ac.uk/id/eprint/118743

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